2/7x+2=x+3

Solution for 2/7x+2=x+3 equation:

2/7x+2=x+3

We move all terms to the left:

2/7x+2-(x+3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

2/7x-x-3+2=0

We multiply all the terms by the denominator


-x*7x-3*7x+2*7x+2=0

Wy multiply elements

-7x^2-21x+14x+2=0

We add all the numbers together, and all the variables

-7x^2-7x+2=0

a = -7; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-7)·2
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{105}}{2*-7}=\frac{7-\sqrt{105}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{105}}{2*-7}=\frac{7+\sqrt{105}}{-14}
$